Entanglement measures and purification procedures

TLDR

The study aims to refine the necessary conditions that any entanglement measure must satisfy. The authors develop improved criteria for entanglement measures, compute them for mixed two‑spin‑½ systems via quantum relative entropy, and provide an efficient numerical method and statistical justification for the approach. They identify a class of entanglement measures, including those derived from quantum relative entropy and the Bures metric, prove key physical properties, and show the measure bounds the number of singlets obtainable by any purification procedure.

Abstract

We improve previously proposed conditions each measure of entanglement has to satisfy. We present a class of entanglement measures that satisfy these conditions and show that the quantum relative entropy and Bures metric generate two measures of this class. We calculate the measures of entanglement for a number of mixed two spin-1/2 systems using the quantum relative entropy, and provide an efficient numerical method to obtain the measures of entanglement in this case. In addition, we prove a number of properties of our entanglement measure that have important physical implications. We briefly explain the statistical basis of our measure of entanglement in the case of the quantum relative entropy. We then argue that our entanglement measure determines an upper bound to the number of singlets that can be obtained by any purification procedure.